Nouveaux procédés d’hyperdéformation pour produire des tôles fines = New severe plastic deformation processes to obtain sheet products

1

THÈSE

Pour l'obtention du titre de

DOCTEUR DE L'UNIVERSITÉ DE LORRAINE

Spécialité : Mécanique et Matériaux

Présentée par : Viet Quoc VU

Nouveaux procédés d’hyperdéformation pour produire des tôles fines

à partir des métaux massifs

New severe plastic deformation processes to obtain sheet products

from bulk metals

Thèse soutenue publiquement l’aout 28, 2020 à 14h, à l’amphithéâtre UFR MIM (Université de

Lorraine-Metz) devant le jury composé de :

Werner Skrotzki Prof., Technische Universität Dresden, Allemagne Rapporteur

Leo Kestens Prof., Ghent University, Belgique Rapporteur

Valéria Mertinger Prof., University of Miskolc, Hongrie Examinateur

Véronique Doquet HDR, Dir. Recheche, LMS, Ecole Polytechnique, France Examinateur

Roxane Massion Dr., LEM3, Université de Lorraine, France Examinateur

Andras Borbely HDR, Ecole des Mines de Saint Etienne, France Examinateur

Laszlo Toth Prof., LEM3, Université de Lorraine, France Directeur de

thèse

LEM3 /LabEx DAMAS - 7 rue Félix Savart F-57070 METZ, France

Université de Lorraine – Pôle M4: matière, matériaux, métallurgie, mécanique

École doctorale C2MP

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Abstract

Severe plastic deformation (SPD) has been acclaimed as an effective technique for

producing materials with superior properties such as high mechanical and fatigue strength, high

wear resistance, and superplasticity. A generic feature of SPD processes is that large strain is

imposed on the processed sample, mostly under high hydrostatic pressure, for transforming a

coarse-grained microstructure into an ultrafine-grained or nano-grained microstructure, which are

unattainable by conventional thermo-mechanical processing. In the present thesis, three SPD

processes namely, plastic flow machining (PFM), high pressure compressive shearing (HPCS) and

friction assisted lateral extrusion process (FALEP) are proposed for producing sheet materials.

PFM is a SPD process capable of producing sheet materials with large shear strain from bulk

samples in one single extrusion step with the assistance of high hydrostatic pressure. The process

was tested on Al1050 samples to study imposed strain, microstructure and texture evolutions, and

mechanical properties. The results are: a high-degree deformation gradient was obtained across

the thickness of the produced Al1050 sheet, with shear strain ranging from 2.5 to 10; UFG

microstructures and simple shear textures with gradient across the thickness of the produced sheet

were presented; the tensile strength of the sheet increased by about a factor of three with a total

elongation of 20%; the average Lankford parameter of the sheet was 0.92, which is much higher

than conventional aluminum sheets obtained by rolling. Modelling and simulation work on PFM

were focused in two parts: mechanical and texture modelling. In the first part, an analytical model

accompanied by finite element simulations was established to gain insight the formation of the

Al1050 sheet under the loading conditions and die geometry. This modelling and simulation set

was able to predict the lateral extrusion ratio and the effect of the applied back pressure and die

geometry on the formation of the sheet and it produced results in agreement with the experiment.

In the second modelling and simulation set, for texture evolution, first, a strain path model was

established; then, two modelling approaches, including viscoplastic self-consistent (VPSC) and

grain fragmentation (GR) were employed for various strain zones across the produced sheet. The

results showed that in the lowest strain zone, the VPSC model produced good agreement with

experiment for the texture. At large strains, the GR model was successful for reproducing the

experimental texture, indicating the importance of incorporating grain fragmentation into large

strain polycrystal modeling. The second proposed SPD technique in thesis was the HPCS; a variant

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of the high pressure sliding (HPS) process. In this thesis, HPCS was applied to ARMCO® steel in

an apparatus in which the shear force, normal force, and shearing distance could be monitored to

allow the stress-strain response to be measured in situ into the steady state work hardening regime.

The results were: the applied compression stress did not result in a purely hydrostatic stress state

in HPCS; the deviatoric stress state progressively approached the simple shear stress state as a

function of strain; the steady state of strain hardening at 1150 MPa, defining a point on the Derby￾plot of dynamic recrystallization; the microstructure features revealed the occurrence of dynamic

recrystallization in the steady state, at room temperature; the grain size was reduced by about a

factor of 170 upon reaching steady state flow conditions; a characteristic bcc simple shear texture

was found; the produced microstructure and texture were uniform throughout the thickness of the

samples. The last studied SPD process was FALEP, a SPD technique in which a bulk sample is

extruded laterally through a channel die with assistance of a friction force to form a sheet with

extremely high plastic imposed strain under high hydrostatic pressure. It was applied to Al1050

bulk samples to produce sheets with very imposed high strain which led to a significant grain

refinement in which the grain size was reduced more than 160 times; to 600 nm after processing.

The produced Al1050 sheet also showed a significant increase in yield strength: by about five

times, and a remarkably high formability with R-value of 1.33, which is exceptionally high for

aluminum.

Key words

Severe plastic deformation (SPD); Plastic flow machining (PFM); High pressure compressive

shearing (HPCS); Friction assisted lateral extrusion process (FALEP); Microstructure evolution;

Mechanical modelling; Texture evolution modeling

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Résumé

L’hyperdéformation (SPD) a été reconnue comme une technique efficace pour produire

des matériaux avec des propriétés supérieures, telles que la résistance mécanique et de fatigue

élevée, meilleur résistance à l’usure, et la superplasticité. Une caractéristique générique des

processus de HD est qu’une extrême déformation est imposée sur l’échantillon, la plupart du temps

sous haute pression hydrostatique, pour transformer la microstructure initiale dans une

microstructure à grain ultrafin, voir nano, qui sont inaccessibles par les traitement

thermomécaniques conventionnels. Dans cette thèse, trois HP procédés, à savoir : l’usinage

plastique (PFM), le cisaillement compressif à haute pression (HPCS) et le processus d’extrusion

latérale assistée par frottement (FALEP), sont proposés pour la production des matériaux en forme

d’une tôle.

PFM est un procédé SPD capable de produire des matériaux en forme de tôle avec une

grande déformation en cisaillement, à partir d’échantillons massifs dans une seule étape

d’extrusion à l’aide d’une pression hydrostatique élevée. Le procédé a été testé sur des échantillons

d’Al1050 pour étudier les évolutions imposées par la déformation ; concernant la microstructure

et de la texture, ainsi que les propriétés mécaniques. Les résultats obtenus sont : un gradient élevé

de déformation a été obtenu à travers l’épaisseur de la feuille Al1050 produite, avec une valeur de

cisaillement allant de 2,5 à 10; des microstructures UFG et des textures simples de cisaillement

avec un gradient à travers l’épaisseur de la feuille produite, la résistance mécanique a augmenté

d’environ un facteur de trois avec un allongement total de 20%; le paramètre Lankford de la feuille

était de 0,92, ce qui est beaucoup plus élevé que les feuilles d’aluminium conventionnelles

obtenues par laminage.

Les travaux de modélisation et de simulation sur PFM ont été concentrés en deux parties

sur : de la modélisation mécanique, et de la texture. Dans la première partie, un modèle analytique

accompagné de simulations d’éléments finis a été mis en place pour mieux comprendre la

formation de la tôle Al1050 sous chargement pour la géométrie de la matrice. Les modélisations

et simulations ont été en mesure de prédire le rapport d’extrusion latérale et l’effet de la pression

arrière appliquée en fonction de la géométrie de la matrice sur la formation de la tôle et ils ont

produit des résultats en accord avec des expériences. Dans le deuxième ensemble de modélisation

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et de simulation, pour l’évolution de la texture, tout d’abord, un modèle de mode de déformation

a été établi ; puis, deux approches de modélisations ; a viscoplastique auto-cohérente (VPSC) et la

fragmentation des grains (GR) ont été employées pour les zones de déformation à travers la tôle

produite.

Les résultats ont montré que dans la zone de la plus faible déformation, le modèle VPSC a

produit un bon accord avec l’expérience pour la texture. Aux plus grandes déformations, c’est le

modèle GR qui a réussi à reproduire la texture expérimentale, ce qui indique l’importance

d’intégrer la fragmentation des grains dans la modélisation polycrystal à grande déformation. La

deuxième SPD technique proposée dans la thèse était le HPCS; une variante du processus de

glissement à haute pression (HPS). Dans cette thèse, l’HPCS a été appliqué à l’acier ARMCO®

dans un appareil dans lequel la force de cisaillement, la force normale, et le déplacement pouvaient

être mesurés pour pouvoir construire la courbe de contrainte-déformation in situ y compris le

régime stationnaire de durcissement.

Les résultats obtenus : la contrainte de compression appliquée n’a pas produit un état de

contrainte purement hydrostatique dans l’HPCS ; l’état de stress déviatorique s’est

progressivement approché l’état de cisaillement simple en fonction de la déformation ; le stade

stationnaire du durcissement à 1150 MPa définissait un point sur le Derby-plot de la

recristallisation dynamique; les caractéristiques de la microstructure ont indiqué l’occurrence de

la recristallisation dynamique dans le stade stationnaire à température ambiante ; la taille du grain

a été réduite d’environ 170 fois dans le stade stationnaire; une texture bcc de cisaillement simple

caractéristique a été trouvée ; la microstructure et la texture produites étaient uniformes tout au

long de l’épaisseur des échantillons.

Le dernier SPD procédé étudié était le FALEP, une technique SPD dans laquelle un

échantillon massif est extrudé latéralement avec l’aide d’une force de friction pour former une tôle

avec une déformation plastique extrêmement grande sous une pression hydrostatique élevée. Le

FALEP a été appliqué à des échantillons massif d’Al1050 pour produire des tôles à très grande

déformation, ce qui a entraîné un raffinement important des grains jusqu’au une taille du grain plus

de 160 fois plus petite ; à 600 nm. La tôle d’Al1050 présentait également une augmentation très

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significative de la résistance : d’environ cinq fois, et une formabilité remarquablement élevée avec

la valeur R de 1,33, ce qui est exceptionnellement élevé pour l’aluminium.

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Acknowledgements

First and foremost, I would like to express my sincere gratitude and heartfelt thanks to my

supervisor, professor Laszlo TOTH, for his tremendous guidance and inspiration throughout my

thesis work. His continuous and friendly guidance has helped me a lot in constantly improving and

expanding my scientific knowledge and research skills. Not only that, he also trained me to play

ping pong and practiced with me on a regular basis. This helped me to stay strong physically and

mentally to become more effective, productive and consistent in learning and researching. His

liveliness and enthusiasm in sports and sharpness in science are a great inspiration for me to grow

stronger and better in life and research. I feel very fortunate to have him as my PhD supervisor.

I am very grateful Professor Yan Beygelzimer who gave me a great deal of help in

developing some mechanical modelling and calculations. I am also thankful Dr. Roman Kulagin

for his great help in some finite element calculations. My thanks should also go to Dr. Jean-Jacques

Fundenberger, Dr. Yajun Zhao and Dr. Cai Chen for their support and cooperation to facilitate my

research work.

I highly appreciate the special help given by Dr. Olivier Perroud, Dr. Julien Guyon, Dr.

Yudong Zhang and Mr. Patrick Moll for their training and help in X-ray diffraction, Microscopy

and tensile testing measurements.

A friendly and supportive working environment always plays an important role at

workplace. I really appreciate many colleagues and friends in LEM3 laboratory for their support

and friendship during my time in the lab. They are Dr. Benoit Beausir, Mrs. Nathalie Niclas, Mrs.

Arlette Jacquiere, Professor Eric Fleury, Dr. Laurent Weiss, Mr. Julien Oury, Dr. Marc Novelli,

Dr. Subrata Panda, Dr. Satyaveer Dhinwal, Mr. Surya N. Kumaran, Mr. Pariyar Abhishek, Dr.

Sudeep Sahoo, Dr. Zhang Chi, Ms. Qiang Chen, Mr. Hailong…I could not mention all of the

names here, but I will remember all of you as very nice colleagues and friends.

I would like to sincerely appreciate all the thesis examiners and reviewers for taking their

time to examine and review this thesis work.

Finally, I would like to thank my family for their unconditional love and support throughout

my PhD study.

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Contents

Abstract......................................................................................................................i

Résumé .................................................................................................................... iii

Acknowledgements..................................................................................................vi

Table of contents ................................................................................................... vii

List of figures............................................................................................................x

List of tables...........................................................................................................xiv

Introduction..............................................................................................................1

Chapter 1 Literature review ...................................................................................3

1.1 History of SPD ......................................................................................................................3

1.2 Main SPD methods...............................................................................................................4

1.2.1 Equal channel angular pressing (ECAP)......................................................................4

1.2.2 High pressure torsion (HPT) .........................................................................................8

1.2.3 Accumulative roll bonding (ARB) ...............................................................................10

1.3 Other SPD processes..........................................................................................................12

1.4 Change in microstructure during SPD processing .........................................................19

1.4.1 Change in grain shape .................................................................................................19

1.4.2 Grain refinement during SPD processing ...................................................................21

1.4.3 Change in disorientation distribution function (DDF)...............................................23

1.5 Change in crystallographic texture during SPD processing ..........................................27

1.5.1 Introduction of texture .................................................................................................27

1.5.2 Texture evolution during plastic deformation.............................................................28

1.5.3 Kinematics of deformation for orientation change .....................................................28

1.5.4 Modelling texture of polycrystals during plastic deformation ...................................31

1.5.4.1 Taylor model...................................................................................................................31

1.5.4.2 Static model....................................................................................................................32

1.5.4.3 Viscoplastic self-consistent (VPSC)............................................................................33

1.5.4.4 Grain fragmentation (GR) model................................................................................33

1.5.5 Texture evolution during SPD processing...................................................................36

1.6 Chapter conclusions...........................................................................................................42

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Chapter 2 Plastic flow machining – Microstructure, strain estimation, texture

and mechanical properties....................................................................................45

2.1 Introduction ........................................................................................................................45

2.2 Working principles and experimental procedures..........................................................45

2.2.1 Working principles of PFM .........................................................................................45

2.2.2 Experimental procedures .............................................................................................47

2.3 Results and discussion........................................................................................................48

2.3.1 Microstructure evolution..............................................................................................48

2.3.2 Texture evolution..........................................................................................................50

2.3.3 Mechanical properties..................................................................................................53

2.3.4 Formability....................................................................................................................53

2.4 Chapter conclusions...........................................................................................................55

Chapter 3 Plastic flow machining (PFM) – Mechanical modelling ..................57

3.1 Introduction ........................................................................................................................57

3.2 Lateral extrusion ratio and experimental results............................................................57

3.3 Numerical simulation of the PFM process.......................................................................62

3.4 Analytical modeling of the PFM process..........................................................................64

3.4.1 Model for the lateral extrusion ratio............................................................................65

3.4.2 Model for the strain gradient .......................................................................................71

3.5 Discussion............................................................................................................................74

3.6 Chapter conclusions...........................................................................................................78

Appendix A: Power dissipation by friction............................................................................78

Appendix B: Minimization of the total power for obtaining the x value ............................81

Chapter 4 Plastic flow machining (PFM) – Texture modelling.........................83

4.1 Introduction ........................................................................................................................83

4.2 Strain path model...............................................................................................................83

4.3 Polycrystal texture modelling............................................................................................86

4.3.1 VPSC approach.............................................................................................................86

4.3.2 Defining the initial texture and initial grain shape inputs .........................................87

4.3.3 Defining strain hardening parameters ........................................................................89

4.3.4 The grain fragmentation model ...................................................................................91

4.3.5 Defining the input velocity gradient tensors................................................................92

4.3.6 Simulation implementation ..........................................................................................93

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4.4 Results and discussion........................................................................................................94

4.5 Chapter conclusions.........................................................................................................100

Chapter 5 The high pressure compressive shearing process...........................101

5.1 Introduction ......................................................................................................................101

5.2 Working principles and experimental setup..................................................................102

5.3 The mechanics of HPCS ..................................................................................................103

5.4 Experimental procedures ................................................................................................108

5.5 Experimental results........................................................................................................110

5.6 Discussion..........................................................................................................................115

5.7 Chapter conclusions.........................................................................................................121

Appendix: Conversion of the Hencky strain into shear strain...........................................122

Chapter 6 The friction assisted lateral extrusion process (FALEP)...............124

6.1 Introduction ......................................................................................................................124

6.2 Working principles...........................................................................................................124

6.3 Strain estimation ..............................................................................................................126

6.4 Example for application of the FALEP on commercially pure aluminum (Al-1050)126

6.4.1 Experimental setup.....................................................................................................126

6.4.2 Microstructure evolution............................................................................................128

6.4.3 Texture evolution........................................................................................................130

6.4.4 Mechanical properties................................................................................................131

6.4.5 Lankford parameter....................................................................................................132

6.5 Chapter conclusions.........................................................................................................133

Thesis conclusions................................................................................................135

Perspectives...........................................................................................................138

References.............................................................................................................139

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List of figures

Fig. 1.1: Schematic illustration of the ECAP working principle.....................................................5

Fig. 1.2: Schematic of the four processing ECAP routes................................................................6

Fig. 1.3: Schematic of the change in the shear plane in four ECAP routes for two cases: a)  = 90

and b)  = 120................................................................................................................................7

Fig. 1.4: Schematic of HPT working principle................................................................................9

Fig. 1.5: Schematic of ARB working principle .............................................................................10

Fig. 1.6: Microstructure of commercially pure aluminum (Al1050) after shear of 4 by HPTT. Black

lines and gray lines depict disorientations of 15 and 5, respectively .........................................20

Fig. 1.7: An illustration of the formation of geometrically necessary dislocations (GNDs),

statistically stored dislocations, geometrically necessary boundaries (GNBs) and incidental

dislocation boundaries (IDBs) .......................................................................................................21

Fig. 1.8: Microstructures of pure copper deformed by ECAP: (a-c) and HPTT (d) at different levels

........................................................................................................................................................23

Fig. 1.9: Grain-to-grain DDF in comparison with pixel-to-pixel DDF in copper processed by three

ECAP passes..................................................................................................................................24

Fig. 1.10: The grain-to-grain DDF as the function of strain for commercially pure aluminum

processed by HPTT........................................................................................................................26

Fig. 1.11: The shear strain as a function of HAGBs fraction for commercially pure aluminum

during simple shear deformation ...................................................................................................26

Fig. 1.12: Decomposition of deformation gradient in large strain theory .....................................29

Fig. 1.13: A shape change from ABCD to A’B

’C

’D

’

of a grain caused by the slip system (n,b). (a-b):

without geometrical constraint and (c): under geometrical constraint. This shape change causes

deformation and rotation of the crystal ............................................................................................29

Fig. 1.14: Shear direction is parallel to slip plane and slip direction, leading to no lattice rotation....30

Fig. 1.15: An illustration of lattice curvature within a grain .........................................................34

Fig. 1.16: An illustration of a cube-shaped grain subdivided into 27 subgrains. The arrows

represent the resultant addition to the lattice rotation for each subgrain. The second and third levels

of subdivision is demonstrated for the cube element at the top corner..........................................35

Fig. 1.17: (a): (111) pole figure displaying the ideal orientations of FCC metals and (b): (110) pole

figure showing the ideal orientations of BCC metals under simple shear deformation ................38

Fig. 1.18: (a): (0002) and

(1010)

pole figures displaying the ideal orientations of HCP metals

under simple shear deformation.....................................................................................................39

Fig. 1.19: Texture evolution of Al1050 processed by HPT at different equivalent strains: a): 0.75,

b): 1.5, c): 3.89, d): 5.31, e): 7.97, f): 11.9, g): 14.85, h): 17.8, i): 99...........................................41

Fig. 1.20: Texture evolution of AA5086 during HPTT as shear strain progresses from 4 to 24…42

Fig. 2.1: (a): Schematic of the principle of the PFM process and (b): a workpiece after processing.

(FD: flow direction, PD: pressing direction and TD: transverse direction)...................................46

Fig. 2.2: Microstructures of (a): initial sample, (b, d, e and f): the 0.65 mm thickness fin and (c):

the top part of the bulk on the plane TD of a deformed sample. ...................................................49

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Fig. 2.3: Next-neighbor grain disorientation distributions for the LSA, MSA and HSA regions of

the fin. For better precision, the data were obtained from large size EBSD maps not from the small

maps shown in Figs. 2.2d-f............................................................................................................50

Fig. 2.4: (111) pole figures for the (a): initial sample, (c): LSA of the fin, (e): MSA of the fin, (g):

HSA of the fin and (i): top part of the deformed bulk. ODF sections are shown for (d): LSA, (f):

MSA, (h): HSA of the fin and (k): top part of the deformed bulk.................................................52

Fig. 2.5: (a): Geometry of tensile specimens. (b) and (c): Engineering stress-strain curves obtained

in tensile tests at 0, 45 and 90 relative to the flow direction (FD) for the initial sample and for

the fin of 0.65 mm thickness. (d) and (e): Vickers hardness measured on the plane TD of the fin

and on the top part of the deformed bulk sample...........................................................................54

Fig. 3.1: Working principles of the PFM process. (a): die geometry, (b): metal flow ..................58

Fig. 3.2: The dependence of the lateral extrusion ratio on the gap-width, for a back-pressure (BP)

of 110 MPa and also without back-pressure..................................................................................60

Fig. 3.3: Results of finite element simulations of the PFM process for the parameters: H0=20 mm;

H1=18 mm; α=120°. The magnitudes of the velocity, strain rate and effective strain (equivalent

strain) are indicated by the respective color codes. (The maximum value of the equivalent strain is

about 4 in all cases)........................................................................................................................64

Fig. 3.4: Schematic of a kinematically admissible velocity field for the flow into the lateral channel

showing the dead metal zone (a). The velocity hodograph is shown in (b)...................................67

Fig. 3.5: The lateral extrusion ratio x as the function of the displacement L1 of the back-pressure

punch for four values of the gap-width h.......................................................................................71

Fig. 3.6: A kinematically admissible velocity field composed of three rigid blocks for the analysis

of the strain distribution in the fin. (a): The rigid blocks with the velocity discontinuity line

segments are identified by 1, 2, 3. Left to the OCB line the material moves with the velocity

U0

.

The ABC triangle is moving with the velocity

U . Above the OCA segment the material moves

with velocity

U2

. α is the die angle and



is the abscissa of the point C. (b): the velocity hodograph

along the CB segment ....................................................................................................................72

Fig. 3.7: The characteristics of the strain distribution for Mode 2, obtained by the analytical model

(continuous lines), and by FE simulations (red dots) for the die angle

0  =120

and for the friction

value of

m = 0.2 . (a): The predicted width of Zone I. (b): The von Mises strain in Zone I. (c): The

von Mises strain in Zone II............................................................................................................74

Fig. 3.8: The dependence of the lateral extrusion ratio on the

h r

parameter in the experiments

with back pressure of 110 MPa, by finite element simulations and also by the analytical model.

........................................................................................................................................................75

Fig. 3.9: The conditional boundaries of the metal flows for the three possible PFM modes: Mode

1:

P P BP BP  1

; Mode 2:

P P P BP BP BP 1 2  

; Mode 3:

P P BP BP  2

........................................................76

Fig. A1. The method of slices showing schematically the stress distribution...............................79

Fig. 4.1: (a): Von Mises strain distribution from finite element simulation. b: Simplified schematic

of the three deformation zones: LSA, MSA, HSA. c: The velocity field from finite elements

together with the reference systems of local shears.......................................................................85

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Fig. 4.2: (a-b): The initial microstructures of Al1050 on the TD-plane and FD-planes, respectively.

(c): The measured {111} pole figure of the initial microstructure on the TD-plane. (d): The {111}

pole figure of 8000 initial grain orientations reproduced from the initial texture for the simulation

input used in the VPSC modelling. (e): The {111} pole figure of the 1000 initial grain orientations

used as initial grains in the grain fragmentation modelling...........................................................88

Fig. 4.3: (a): The geometry of the Al1050 sample subjected to free-end torsion test. (b): The strain

hardening curve in simple shear deformation in the free end torsion test, with a comparison

between simulation and experiment...............................................................................................90

Fig. 4.4: {111} pole figures for LSA, MSA and HSA obtained from experiment and from

simulations using the VPSC and GR modelling ...........................................................................98

Fig. 4.5: ODF sections for LSA, MSA and HSA obtained from experiment and from simulations

using the VPSC and GR modelling. The reference system is the fix XYZ sample system...........99

Fig. 5.1: (a): Schematic figure for the experimental HPCS setup. (b): The two samples after the

first pass deformation ..................................................................................................................102

Fig. 5.2: Schematic figure showing the dimensions and the forces applied on the upper specimen

......................................................................................................................................................104

Fig. 5.3: The initial grain-state of the material (a) and its crystallographic texture in a {110} pole

figure (b) ......................................................................................................................................110

Fig. 5.4: Stress–strain curves obtained by HPCS for ARMCO® steel in three consecutive passes

up to an equivalent strain of 33.34...............................................................................................110

Fig. 5.5: (a)-(b): IPF maps after the first and third passes. (c)-(d): Ellipticity and grain size

distributions. (e)-(f): Next-neighbor disorientation distributions................................................112

Fig. 5.6: The crystallographic textures in {110} pole figures, and the ODFs in two sections of the

Euler orientation space (top row: 2=0°, bottom row: 2=45°). SPN and SD denote the orientations

of the shear plane normal and the shear direction, respectively ..................................................114

Fig. 5.7: (a): The evolution of the non-zero stress components of the stress tensor during HPCS of

ARMCO® steel during the first pass. The value of the hydrostatic stress

 h

is equal to

 33

. The

curve indicated by



is the shear stress.  is the ratio of the deviator stresses corresponding to the

compression and the shear. (b): The shear and compression strains as a function of the equivalent

strain during the first pass. (c): The rate of strain hardening as a function of stress (‘Kocks-Mecking

plot’) from (a). (d): The evolution of the stress state during HPCS of ARMCO® steel in the S11-S12

section of the von Mises yield surface.........................................................................................116

Fig. 6.1: Schematic of the FALEP process..................................................................................125

Fig. 6.2: Experimental setup (a) and (b), and example of a half-extruded Al-1050 sample (c)…127

Fig. 6.3: (a): Experimental setup for T-NECAP for Al-1050. (b): The sample obtained after

processing ....................................................................................................................................128

Fig. 6.4: (a): EBSD microstructure of the initial sample; (b): SEM microstructure across the

thickness of the produced fin; (c), (d) and (e): EBSD microstructures of the bottom, middle and

top areas of the Al-1050 produced fin, respectively ....................................................................129

Fig. 6.5: Next-neighbor grain disorientation distributions measured in the top, middle and bottom

areas of the Al-1050 produced fin ...............................................................................................130

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Fig. 6.6: Crystallographic texture for the initial sample (a), key figure (b) for the ODFs sections

in (d): pole figure (c) and ODF (d) after FALEP processing.......................................................130

Fig. 6.7: (a): Engineering tensile stress-strain curves of the initial sample and the FALEP￾processed 1 mm thickness Al-1050 fin obtained at 0°, 45° and 90° with respect to the flow direction

(FD), at room temperature. (b): The geometry of the tensile specimens.....................................131

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List of tables

Table 1.1: Geometrical changes, total reduction and accumulated equivalent strain in a series of

ARB passes of two pieces of 1-mm-thick strip .............................................................................11

Table 1.2: SPD processes developed from the ECAP technique ..................................................13

Table 1.3: SPD processes developed from the HPT technique.....................................................15

Table 1.4: Some rolling-based SPD processes..............................................................................17

Table 1.5: Direct-extrusion-based SPD processes ........................................................................18

Table 1.6: Machining-based SPD process.....................................................................................19

Table 1.7: Ideal texture orientations with Euler angles for different crystal structures: FCC, BCC

and HCP in simple shear deformation ...........................................................................................37

Table 2.1: Ideal orientations of simple shear textures for FCC materials. (hkl) is perpendicular to

the shear plane and [uvw] is parallel to the shear direction...........................................................51

Table 2.2: R values measured in PFM processed CP aluminum ..................................................55

Table 4.1: Directions and shear strains of the various shear planes in the deformation zone. The

shear strain values were obtained from the shear formula (Eq. 4.1), except for the friction-induced

shears, indicated by *, which were estimated from the simulations..............................................85

Table 4.2: Shear plane sequences and accumulated total shears for the three shear zones ..........86

Table 4.3: Orientations of the experimental and simulated textures in the different deformation

zones as defined by the rotation angles between the FD sample axis and the shear plane (SP)

identified in the pole figures of Fig. 4.4. (The values are in degrees.) ..........................................95

Table 5.1: The equivalent strain and the sample thickness in multipass HPCS for the initial

geometry

0

t

=2 mm,

0

l

=10 mm and a shear displacement

s

=10 mm........................................ 108

Table 5.2: The parameters of the multi-pass HPCS testing on ARMCO® steel ........................109

Table 5.3: Average grain sizes obtained after HPCS of ARMCO® steel. Unit is [nm]..............111

Table 5.4: The Miller indices of the main ideal orientations of simple shear textures for BCC

materials and their location in the 2=45° section of Euler orientation space (for shear in direction

of axis 1 and with shear plane normal oriented in direction 2)....................................................115

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